5w^2+4-w-6=0

Solution for 5w^2+4-w-6=0 equation:

5w^2+4-w-6=0

We add all the numbers together, and all the variables

5w^2-1w-2=0

a = 5; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·5·(-2)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{41}}{2*5}=\frac{1-\sqrt{41}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{41}}{2*5}=\frac{1+\sqrt{41}}{10}
$